In a recent post we described a paper written by Dustin Marshall and Craig White and published in Trends in Ecology and Evolution (TREE). The published article was called “Have we outgrown the existing models of growth?” In it, Dustin and Craig suggest that the growth dynamics that biologists have long sought to understand probably emerge simply from hyperallometric scaling of reproduction.

Daniel Pauly is a fisheries scientist from the University of British Columbia and is a proponent of the Gill-Oxygen Limitation Theory (GOLT) of growth. This theory applies to water-breathing animals and is structured around the proposition that growth is necessarily constrained by the size of the gills and the oxygen they are able to extract from the water.

Professor Pauly argues in a letter to TREE that there is a good reason why growth is not considered to be influenced by reproduction in the context of GOLT. While he agrees that reproductive output tends to scale hyperallometrically in fish, he does not agree that fish slow their growth because they allocate increasingly more to reproduction. Instead, he thinks that as growth slows (due to oxygen limitation caused by physical constraints on gill size) increased allocation of resources is directed to reproduction.

In their rebuttal, Dustin and Craig summarise their difference in opinion as one of causality; while Professor Pauly argues that body size in fish is limited by gill area, they believe that organs evolve to provide capacity to meet an organisms requirements. Or, in other words, the trait of body size is the product of selection whereby the size of an organisms is the best it can be to maximise fitness in a particular environment. Most importantly, taken to its logical extension, Dustin and Craig argue that Pauly’s own arguments imply fish reproduction should decrease with size.

In a separate letter, Michael Kearney from the University of Melbourne suggests that a radical revision of growth models is premature. In this case, Associate Professor Kearney suggests that a mechanistic modelling approach (such as Dynamic Energy Budget theory) based on a thermodynamically explicit theory of metabolism is better suited to understanding growth than the phenomenological modelling approach proposed by Dustin and Craig.

While Assoc. Prof. Kearney argues that the Dynamic Energy Budget model can incorporate hyperallometric scaling by adjusting the ‘rules’ governing how much energy is allocated to reproduction, Craig and Dustin say that to do this requires a phenomenological approach and is an unjustified post hoc model fitting solution. According to Craig and Dustin, this means that Assoc. Prof. Kearney’s model is not strictly mechanistic, with some parameters estimated by fitting mechanistic functions and some parameters requiring empirical data (a phenomenological approach).

But there is some agreement. Dustin, Craig and Michael Kearney are all interested in seeing studies of growth and metabolism that are conducted in the context of a full accounting of energy and mass balances (food in, changes in length and weight, respiration, faeces and eggs out) to continue improving our understanding of why organisms are the size they are.

You can read the original article and the follow-up letters.